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M15, How Old Are You?

Jimmy Dreese, Fall 2009

This fall, John Weiss and I decided to try to use CCD images to determine the age of star clusters. This is a project I'd tried before but hadn't had much success with, mostly because last year, Cindy and I had had trouble getting decent images of the clusters and so had been unable to move on to image analysis. This time, I wanted to see if I could actually find something.

A few weeks into fall term, I had my plan and was ready to take some images. I planned to image three globular clusters (which ones I would image depended on which ones were up on the night I went observing) using B, V, and R filters in the CCD camera (as opposed to normal R, B, and G filters, which make for great images but aren't as useful for the kind of analysis I was planning on doing).

I would then use the B and V images to construct Hertzsprung-Russell (H-R) diagrams of the clusters. H-R diagrams plot stars' luminosity against its spectral type (color). So basically, I could determine the star's color by the difference in B and V magnitudes of the stars in my images. The luminosity is collected by measuring the relative brightnesses of stars in my image and scaling them against a standard star whose luminosity we already know.

So on October 12, I headed over to Goodsell a little before 11:00 PM, and with the help of my friends Ben and Carrie, had the telescope mounted, the camera focused, and a likely cluster picked out by 11:45. I chose to start with M15, because this is a relatively bright globular cluster, and it was high enough in the sky that I thought I could catch a good image of it. After M15, I imaged M2 and M92, other globular clusters in the area. Unfortunately, these two clusters were low enough in the sky by this point that the images weren't usable. I proceeded, however, with my M15 images.

I took ten exposures each of 35 seconds with the B and V filters through an 8-inch Meade telescope. During the next few days, I aligned and mean-stacked most of the exposures (a few bad-quality exposures were thrown out). Stacking multiple exposures allowed me to decrease some of the noise in the final images and get brighter images with which to work.

Here's my B-filter image of M15:

 

JDreeseM15-1

 

And the same cluster through the V-filter:

 

JDreeseM15-2

 

These images are definitely not perfect – I could have focused better, and it was a windy night, which led to some camera-movement and trailing of the stars. It's also possible that some distortion from exposure to exposure stopped the exposures from being precisely aligned (though I did align them manually and was careful to align them as closely as possible). But still, I had images, and I proceeded on to analysis!

I started by finding a standard star in the image against which to measure the brightness of the other stars. I chose HD 204712 (the bright star above and left of the cluster in both images). The Simbad star database told me its B magnitude is 8.144; its V magnitude is 7.616.

 

JDreeseM15-3

 

I started by choosing 26 stars to analyze and assemble into an H-R diagram (stars A-Z) and used Equinox Image to compute their magnitudes relative to HD 204712. Once I'd gathered B and V magnitudes for all 26 stars, I assembled them into an observational H-R diagram. See the bottom of this page for all of the data. Color appears on the x-axis, luminosity on the y-axis.

 

JDreeseM15-4

 

What we're looking for is what's called the main sequence turn-off point. In an H-R diagram, most stars line up along a straight diagonal line called the main sequence. For most of their lives, stars appear on the main sequence. But when a star begins to run out of hydrogen fuel and die, the relationship between the color and luminosity diverges from the main sequence, resulting in different types of stars like red giants and white dwarfs.

We know that bluer stars (those farther left in the graph) die sooner, because they use up their fuel more quickly. So stars should begin to leave the main sequence starting at the left and moving towards the right. If you find the turn-off point where the stars to the left of it have left the main sequence and stars to its right are still on the main sequence, you can use this turn-off point to determine the age of the star cluster.

Unfortunately, my graph doesn't appear to have a main sequence turn-off point!

Looking back at the stars I selected, I wonder if this could be part of the problem. I selected a lot of stars pretty far away from the cluster's center – what if some of these stars aren't actually part of the cluster, so including them in the H-R diagrams skewed the data? Another worry was that I chose these stars because I could see them in the images. Since brighter stars are more likely to appear in an image, I was more likely to select bright stars for my sample and so could be looking at an uncharacteristically blue group of stars that aren't on the main sequence any more at all. I decided to try a new sampling of stars. This time, I tried to stick closer to the cluster's center and to select some dimmer stars as well. These are stars 1-30.

 

JDreeseM15-5

 

As you can see, there's still no clear turn-off point, let alone a main sequence. In a last-ditch effort, I combined the two samples:

 

JDreeseM15-6

 

John and I weren't able to conclusively figure out anything from this graph. We looked at another H-R diagram of M15 and considered where our data might be falling on this graph, but we would need more data in order to be conclusive. Ideally, we would take more images that cut down on trailing and focus-error. Better quality images might result in better data.

Even though we didn't actually end up determining the age of M15, the project was still really valuable: we did successfully compile an observational H-R diagram, and I got the chance to do some astrometric analysis from CCD images. If I continue this project in the future, I'll want to capture some clearer images from which to work and perhaps look at open- as well as globular clusters.

 Here's the data from which I compiled my H-R diagrams!

Star name B magnitude V magnitude Star name B magnitude V magnitude
HD 204712 8.144 7.616 1 14.552 14.58
A 12.576 12.956 2 14.28 14.548
B 12.479 12.304 3 13.162 13.665
C 12.847 13.497 4 12.878 13.222
D 12.868 13.532 5 13.991 14.267
E 11.804 14.006 6 14.102 13.969
F 13.413 14.222 7 13.773 14.256
G 11.623 12.734 8 13.813 14.407
H 12.18 13.518 9 13.932 14.216
I 12.776 14.371 10 13.702 14.157
J 14.462 13.768 11 13.22 13.514
K 12.985 13.411 12 12.294 13.09
L 11.788 13.496 13 13.752 13.915
M 13.506 13.848 14 13.63 13.342
N 13.072 14.659 15 14.595 13.661
O 13.025 13.791 16 13.204 13.66
P 13.229 14.667 17 13.963 14.296
Q 12.712 13.672 18 13.599 13.956
R 12.3 14.314 19 13.818 14.125
S 12.993 13.475 20 14.304 14.432
T 12.747 13.926 21 13.477 13.835
U 13.185 13.983 22 14.561 14.428
V 12.969 13.642 23 14.189 14.223
W 13.296 14.71 24 14.323 14.54
X 12.74 13.538 25 14.708 14.424
Y 13.419 14.276 26 14.85 15.113
Z 12.919 13.433 28 14.835 14.291
29 14.574 14.434
30 13.872 14.201